How do I find the volume of a sphere inscribed in a cube with each edge 4 cm
Isn't the diameter of the sphere equal to the length of the cube, it it fits snugly ?
So r = 2 cm
Volumesphere = (4/3)pi(r^3)
To find the volume of a sphere inscribed in a cube, we can follow these steps:
1. Determine the edge length of the cube. In this case, it is given that each edge of the cube is 4 cm.
2. Find the diameter of the inscribed sphere. The diameter of the sphere is equal to the edge length of the cube since it is inscribed perfectly. Therefore, the diameter of the sphere is also 4 cm.
3. Calculate the radius of the sphere. The radius is half of the diameter, so in this case, the radius of the sphere is 4 cm / 2 = 2 cm.
4. Use the formula for the volume of a sphere, which is V = (4/3) * π * r^3, where π is a mathematical constant (approximately equal to 3.14159) and r is the radius of the sphere.
Plugging in the values, we get V = (4/3) * 3.14159 * (2 cm)^3.
Simplifying further, V = (4/3) * 3.14159 * 8 cm^3.
5. Calculate the final value to get the volume of the inscribed sphere. V ≈ 33.51032 cm^3.
Therefore, the volume of the sphere inscribed in a cube with each edge measuring 4 cm is approximately 33.51032 cm^3.